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    <title>penlaur</title>
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    <center>Scilab Function</center>
    <div align="right">Last update : 20/12/2004</div>
    <p>
      <b>penlaur</b> -  Laurent coefficients of matrix pencil</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>[Si,Pi,Di,order]=penlaur(Fs)  </tt>
      </dd>
      <dd>
        <tt>[Si,Pi,Di,order]=penlaur(E,A)  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>Fs</b>
        </tt>: a regular pencil <tt>
          <b>s*E-A</b>
        </tt>
      </li>
      <li>
        <tt>
          <b>E, A</b>
        </tt>: two real square matrices</li>
      <li>
        <tt>
          <b>Si,Pi,Di</b>
        </tt>: three real square matrices</li>
      <li>
        <tt>
          <b>order</b>
        </tt>: integer</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
      <tt>
        <b>penlaur</b>
      </tt> computes the first Laurent coefficients of <tt>
        <b>(s*E-A)^-1</b>
      </tt> at
    infinity.</p>
    <p>
      <tt>
        <b>(s*E-A)^-1 = ... + Si/s - Pi - s*Di + ...</b>
      </tt> at <tt>
        <b>s</b>
      </tt> = infinity.</p>
    <p>
      <tt>
        <b>order</b>
      </tt> = order of the singularity (order=index-1).</p>
    <p>
    The matrix pencil <tt>
        <b>Fs=s*E-A</b>
      </tt> should be invertible.</p>
    <p>
    For a index-zero pencil, <tt>
        <b>Pi, Di,...</b>
      </tt> are zero and <tt>
        <b>Si=inv(E)</b>
      </tt>.</p>
    <p>
    For a index-one pencil (order=0),<tt>
        <b>Di</b>
      </tt> =0.</p>
    <p>
    For higher-index pencils, the terms <tt>
        <b> -s^2 Di(2), -s^3    Di(3),... </b>
      </tt> are given by:</p>
    <p>
      <tt>
        <b> Di(2)=Di*A*Di</b>
      </tt>, <tt>
        <b> Di(3)=Di*A*Di*A*Di</b>
      </tt> (up
    to <tt>
        <b>Di(order)</b>
      </tt>).</p>
    <h3>
      <font color="blue">Remark</font>
    </h3>
    <dl>
      <p>
    Experimental version: troubles when bad conditioning of <tt>
          <b>so*E-A</b>
        </tt>
      </p>
    </dl>
    <h3>
      <font color="blue">Examples</font>
    </h3>
    <pre>

F=randpencil([],[1,2],[1,2,3],[]);
F=rand(6,6)*F*rand(6,6);[E,A]=pen2ea(F);
[Si,Pi,Di]=penlaur(F);
[Bfs,Bis,chis]=glever(F);
norm(coeff(Bis,1)-Di,1)
 
  </pre>
    <h3>
      <font color="blue">See Also</font>
    </h3>
    <p>
      <a href="glever.htm">
        <tt>
          <b>glever</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="pencan.htm">
        <tt>
          <b>pencan</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="rowshuff.htm">
        <tt>
          <b>rowshuff</b>
        </tt>
      </a>,&nbsp;&nbsp;</p>
    <h3>
      <font color="blue">Author</font>
    </h3>
    <p>F. Delebecque INRIA(1988,1990) ;   </p>
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